Problem: Solve for $k$, $ -\dfrac{5}{k^2} = -\dfrac{6}{4k^2} - \dfrac{5k + 2}{k^2} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $k^2$ $4k^2$ and $k^2$ The common denominator is $4k^2$ To get $4k^2$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{5}{k^2} \times \dfrac{4}{4} = -\dfrac{20}{4k^2} $ The denominator of the second term is already $4k^2$ , so we don't need to change it. To get $4k^2$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{5k + 2}{k^2} \times \dfrac{4}{4} = -\dfrac{20k + 8}{4k^2} $ This give us: $ -\dfrac{20}{4k^2} = -\dfrac{6}{4k^2} - \dfrac{20k + 8}{4k^2} $ If we multiply both sides of the equation by $4k^2$ , we get: $ -20 = -6 - 20k - 8$ $ -20 = -20k - 14$ $ -6 = -20k $ $ k = \dfrac{3}{10}$